{"id":1122,"date":"2018-02-25T10:47:07","date_gmt":"2018-02-25T02:47:07","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1122"},"modified":"2018-02-25T10:47:07","modified_gmt":"2018-02-25T02:47:07","slug":"perfectly-inelastic-collisions-in-one-dimension-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/perfectly-inelastic-collisions-in-one-dimension-problems-and-solutions.htm","title":{"rendered":"Inelastic collisions in one dimension \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A 30-gram bullet moving at 30 m\/s collide a 1-kg block at rest. Determine the speed of the block if the bullet and the block lock together as a result of the collision<\/a>.<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Mass<\/span><\/span><\/a> of bullet <\/span><\/span>(m<\/span><\/span>1<\/span><\/sub>) = 30 gram = 0.03 kg<\/span><\/span><\/p>\n

Mass <\/span><\/span>of block <\/span><\/span>(m<\/span><\/span>2<\/span><\/sub>) = 1 kg<\/span><\/span><\/p>\n

Initial speed of bullet (<\/span><\/span>v<\/span><\/span>1<\/span><\/sub>) = 30 m\/s<\/span><\/span><\/p>\n

initial speed of block <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>) = 0 (<\/span><\/span>block at rest<\/span><\/span>)<\/span><\/span><\/p>\n

Wanted<\/u><\/span><\/span> : <\/span><\/span>the speed of bullet and block after collision <\/span><\/span>(v\u2019)<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/p>\n

m<\/span><\/span>1 <\/span><\/sub>v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub> = (m<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub>) v\u2019<\/span><\/span><\/p>\n

(0.03)(30) + (1)(0) = (0.03 + 1) v\u2019<\/span><\/span><\/p>\n

0.9 + 0 = 1.03 v\u2019<\/span><\/span><\/p>\n

0.9 = 1,03 v\u2019<\/span><\/span><\/p>\n

v\u2019 = 0.9 \/ 1,03<\/span><\/span><\/p>\n

v\u2019 = 0.87 m\/s <\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>Billiard ball A of mass 2 kg moving with speed v<\/span><\/span>A<\/span><\/sub> = 6 m.s<\/span><\/span>\u22121 <\/span><\/span><\/sup>collides head-on with ball B of equal mass. If the collision is perfectly inelastic, what are the speeds of the two balls after the collision.<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Mass A (m<\/span><\/span>A<\/span><\/sub>) = 2 kg<\/span><\/span><\/p>\n

Mass B (m<\/span><\/span>B<\/span><\/sub>) = 2 kg<\/span><\/span><\/p>\n

Initial speed of ball A <\/span><\/span>(v<\/span><\/span>A<\/span><\/sub>) = -6 m\/s<\/span><\/span><\/p>\n

Initial speed of ball B <\/span><\/span>(v<\/span><\/span>B<\/span><\/sub>) = 4 m\/s<\/span><\/span><\/p>\n

The plus and minus sign indicates that the objects moves in opposite direction.<\/i><\/span><\/span><\/p>\n

Wanted<\/u>:<\/u> the speeds of the two balls after the collision. (v\u2019)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

m<\/span><\/span>A<\/span><\/sub> v<\/span><\/span>A<\/span><\/sub> + m<\/span><\/span>B<\/span><\/sub> v<\/span><\/span>B<\/span><\/sub> = (m<\/span><\/span>A<\/span><\/sub>\u2019 + m<\/span><\/span>B<\/span><\/sub>) v\u2019<\/span><\/span><\/p>\n

(2)(-6) + (2)(4) = (2 + 2) v\u2019<\/span><\/span><\/p>\n

-12 + 8 = 4 v\u2019<\/span><\/span><\/p>\n

-4 = 4 v\u2019<\/span><\/span><\/p>\n

v\u2019 = -4 \/ 4<\/span><\/span><\/p>\n

v\u2019 = -1 m\/s<\/span><\/span><\/p>\n

<\/p>\n

3. m<\/span><\/span>1<\/span><\/sub> = 3 kg <\/span><\/span>and <\/span><\/span>m<\/span><\/span>2<\/span><\/sub> = 4 kg <\/span><\/span>approach each other in opposite direction with speed of <\/span><\/span>v<\/span><\/span>1<\/span><\/sub> = 10 m\/s <\/span><\/span>and <\/span><\/span>v<\/span><\/span>2<\/span><\/sub> = 12 m\/s. <\/span><\/span>If the collision is perfectly inelastic, what are the speeds of the two balls after the collision.<\/span><\/span><\/p>\n

Known :<\/span><\/span><\/u><\/p>\n

Mass <\/span><\/span>object <\/span><\/span>1 (m<\/span><\/span>1<\/span><\/sub>) = 3 kg<\/span><\/span><\/p>\n

Mass <\/span><\/span>object <\/span><\/span>2 (m<\/span><\/span>2<\/span><\/sub>) = 4 kg<\/span><\/span><\/p>\n

The speed of object 1<\/span><\/span> (v<\/span><\/span>1<\/span><\/sub>) = -10 m\/s<\/span><\/span><\/p>\n

The speed of object 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>) = 12 m\/s<\/span><\/span><\/p>\n

Wanted <\/u><\/span><\/span>: <\/span><\/span>the speed after collision<\/span><\/span> (v\u2019)<\/span><\/span><\/p>\n

Solution :<\/span><\/span><\/u><\/p>\n

m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub> = (m<\/span><\/span>1<\/span><\/sub>\u2019 + m<\/span><\/span>2<\/span><\/sub>) v\u2019<\/span><\/span><\/p>\n

(3)(-10) + (4)(12) = (3 + 4) v\u2019<\/span><\/span><\/p>\n

-30 + 48 = 7 v\u2019<\/span><\/span><\/p>\n

18 = 7 v\u2019<\/span><\/span><\/p>\n

v\u2019 = 18 \/ 7<\/span><\/span><\/p>\n

v\u2019 = 2.6 m\/s<\/span><\/span><\/p>\n

[wpdm_package id=’1157′]<\/p>\n

    \n
  1. Linear momentum problems and solutions<\/a><\/li>\n
  2. Momentum and impulse problems and solutions<\/a><\/li>\n
  3. Perfectly elastic collisions in one dimension problems and solutions<\/a><\/li>\n
  4. Perfectly inelastic collisions in one dimension problems and solutions<\/a><\/li>\n
  5. Inelastic collisions in one dimension problems and solutions<\/a><\/li>\n<\/ol>\n

    <\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

    1. A 30-gram bullet moving at 30 m\/s collide a 1-kg block at rest. Determine the speed of the block if the bullet and the block lock together as a result of the collision. Known : Mass of bullet (m1) = 30 gram = 0.03 kg Mass of block (m2) = 1 kg Initial speed … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Inelastic collisions in one dimension \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1122","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=1122"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1122\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}